{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiclass Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example show shows how to use `tsfresh` to extract and select useful features from timeseries in a multiclass classification example.\n",
    "\n",
    "We use an example dataset of human activity recognition for this.\n",
    "The dataset consists of timeseries for 7352 accelerometer readings. \n",
    "Each reading represents an accelerometer reading for 2.56 sec at 50hz (for a total of 128 samples per reading). Furthermore, each reading corresponds one of six activities (walking, walking upstairs, walking downstairs, sitting, standing and laying).\n",
    "\n",
    "For more information go to https://archive.ics.uci.edu/ml/datasets/Human+Activity+Recognition+Using+Smartphones\n",
    "\n",
    "This notebook follows the example in [the first notebook](./01%20Feature%20Extraction%20and%20Selection.ipynb), so we will go quickly over the extraction and focus on the more interesting feature selection in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "from tsfresh import extract_features, extract_relevant_features, select_features\n",
    "from tsfresh.utilities.dataframe_functions import impute\n",
    "\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import classification_report\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and visualize data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tsfresh.examples.har_dataset import download_har_dataset, load_har_dataset, load_har_classes\n",
    "\n",
    "# fetch dataset from uci\n",
    "download_har_dataset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "        0         1         2         3         4         5         6    \\\n0  0.000181  0.010139  0.009276  0.005066  0.010810  0.004045  0.004757   \n1  0.001094  0.004550  0.002879  0.002247  0.003305  0.002416  0.001619   \n2  0.003531  0.002285 -0.000420 -0.003738 -0.006706 -0.003148  0.000733   \n3 -0.001772 -0.001311  0.000388  0.000408 -0.000355  0.000998  0.001109   \n4  0.000087 -0.000272  0.001022  0.003126  0.002284  0.000885  0.001933   \n\n        7         8         9    ...       118       119       120       121  \\\n0  0.006214  0.003307  0.007572  ...  0.001412 -0.001509  0.000060  0.000435   \n1  0.000981  0.000009 -0.000363  ... -0.000104 -0.000141  0.001333  0.001541   \n2  0.000668  0.002162 -0.000946  ...  0.000661  0.001853 -0.000268 -0.000394   \n3 -0.003149 -0.008882 -0.010483  ...  0.000458  0.002103  0.001358  0.000820   \n4  0.002270  0.002247  0.002175  ...  0.002529  0.003518 -0.000248 -0.002761   \n\n        122       123       124       125       126       127  \n0 -0.000819  0.000228 -0.000300 -0.001147 -0.000222  0.001576  \n1  0.001077 -0.000736 -0.003767 -0.004646 -0.002941 -0.001599  \n2 -0.000279 -0.000316  0.000144  0.001246  0.003117  0.002178  \n3 -0.000212 -0.001915 -0.001631 -0.000867 -0.001172 -0.000028  \n4  0.000252  0.003752  0.001626 -0.000698 -0.001223 -0.003328  \n\n[5 rows x 128 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>0</th>\n      <th>1</th>\n      <th>2</th>\n      <th>3</th>\n      <th>4</th>\n      <th>5</th>\n      <th>6</th>\n      <th>7</th>\n      <th>8</th>\n      <th>9</th>\n      <th>...</th>\n      <th>118</th>\n      <th>119</th>\n      <th>120</th>\n      <th>121</th>\n      <th>122</th>\n      <th>123</th>\n      <th>124</th>\n      <th>125</th>\n      <th>126</th>\n      <th>127</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.000181</td>\n      <td>0.010139</td>\n      <td>0.009276</td>\n      <td>0.005066</td>\n      <td>0.010810</td>\n      <td>0.004045</td>\n      <td>0.004757</td>\n      <td>0.006214</td>\n      <td>0.003307</td>\n      <td>0.007572</td>\n      <td>...</td>\n      <td>0.001412</td>\n      <td>-0.001509</td>\n      <td>0.000060</td>\n      <td>0.000435</td>\n      <td>-0.000819</td>\n      <td>0.000228</td>\n      <td>-0.000300</td>\n      <td>-0.001147</td>\n      <td>-0.000222</td>\n      <td>0.001576</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.001094</td>\n      <td>0.004550</td>\n      <td>0.002879</td>\n      <td>0.002247</td>\n      <td>0.003305</td>\n      <td>0.002416</td>\n      <td>0.001619</td>\n      <td>0.000981</td>\n      <td>0.000009</td>\n      <td>-0.000363</td>\n      <td>...</td>\n      <td>-0.000104</td>\n      <td>-0.000141</td>\n      <td>0.001333</td>\n      <td>0.001541</td>\n      <td>0.001077</td>\n      <td>-0.000736</td>\n      <td>-0.003767</td>\n      <td>-0.004646</td>\n      <td>-0.002941</td>\n      <td>-0.001599</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.003531</td>\n      <td>0.002285</td>\n      <td>-0.000420</td>\n      <td>-0.003738</td>\n      <td>-0.006706</td>\n      <td>-0.003148</td>\n      <td>0.000733</td>\n      <td>0.000668</td>\n      <td>0.002162</td>\n      <td>-0.000946</td>\n      <td>...</td>\n      <td>0.000661</td>\n      <td>0.001853</td>\n      <td>-0.000268</td>\n      <td>-0.000394</td>\n      <td>-0.000279</td>\n      <td>-0.000316</td>\n      <td>0.000144</td>\n      <td>0.001246</td>\n      <td>0.003117</td>\n      <td>0.002178</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>-0.001772</td>\n      <td>-0.001311</td>\n      <td>0.000388</td>\n      <td>0.000408</td>\n      <td>-0.000355</td>\n      <td>0.000998</td>\n      <td>0.001109</td>\n      <td>-0.003149</td>\n      <td>-0.008882</td>\n      <td>-0.010483</td>\n      <td>...</td>\n      <td>0.000458</td>\n      <td>0.002103</td>\n      <td>0.001358</td>\n      <td>0.000820</td>\n      <td>-0.000212</td>\n      <td>-0.001915</td>\n      <td>-0.001631</td>\n      <td>-0.000867</td>\n      <td>-0.001172</td>\n      <td>-0.000028</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.000087</td>\n      <td>-0.000272</td>\n      <td>0.001022</td>\n      <td>0.003126</td>\n      <td>0.002284</td>\n      <td>0.000885</td>\n      <td>0.001933</td>\n      <td>0.002270</td>\n      <td>0.002247</td>\n      <td>0.002175</td>\n      <td>...</td>\n      <td>0.002529</td>\n      <td>0.003518</td>\n      <td>-0.000248</td>\n      <td>-0.002761</td>\n      <td>0.000252</td>\n      <td>0.003752</td>\n      <td>0.001626</td>\n      <td>-0.000698</td>\n      <td>-0.001223</td>\n      <td>-0.003328</td>\n    </tr>\n  </tbody>\n</table>\n<p>5 rows × 128 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "df = load_har_dataset()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = load_har_classes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is not in a typical time series format so far: \n",
    "the columns are the time steps whereas each row is a measurement of a different person.\n",
    "\n",
    "Therefore we bring it to a format where the time series of different persons are identified by an `id` and are order by time vertically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"id\"] = df.index\n",
    "df = df.melt(id_vars=\"id\", var_name=\"time\").sort_values([\"id\", \"time\"]).reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   id time     value\n0   0    0  0.000181\n1   0    1  0.010139\n2   0    2  0.009276\n3   0    3  0.005066\n4   0    4  0.010810",
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     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.title('accelerometer reading')\n",
    "plt.plot(df[df[\"id\"] == 0].set_index(\"time\").value)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "Feature Extraction: 100%|██████████| 20/20 [00:13&lt;00:00,  1.43it/s]\n"
    }
   ],
   "source": [
    "# only use the first 500 ids to speed up the processing\n",
    "X = extract_features(df[df[\"id\"] < 500], column_id=\"id\", column_sort=\"time\", impute_function=impute)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   value__variance_larger_than_standard_deviation  value__has_duplicate_max  \\\n0                                             0.0                       0.0   \n1                                             0.0                       0.0   \n2                                             0.0                       0.0   \n3                                             0.0                       0.0   \n4                                             0.0                       0.0   \n\n   value__has_duplicate_min  value__has_duplicate  value__sum_values  \\\n0                       0.0                   0.0           0.290392   \n1                       0.0                   0.0           0.022239   \n2                       0.0                   0.0           0.054796   \n3                       0.0                   0.0           0.042157   \n4                       0.0                   0.0          -0.024980   \n\n   value__abs_energy  value__mean_abs_change  value__mean_change  \\\n0           0.001766                0.001435            0.000011   \n1           0.000506                0.001323           -0.000021   \n2           0.001106                0.001827           -0.000011   \n3           0.000932                0.001470            0.000014   \n4           0.000525                0.001215           -0.000027   \n\n   value__mean_second_derivative_central  value__median  ...  \\\n0                              -0.000032       0.002025  ...   \n1                              -0.000008       0.000110  ...   \n2                               0.000001       0.000627  ...   \n3                               0.000003       0.000269  ...   \n4                              -0.000007      -0.000144  ...   \n\n   value__fourier_entropy__bins_2  value__fourier_entropy__bins_3  \\\n0                        0.079487                        0.079487   \n1                        0.187031                        0.490294   \n2                        0.307845                        0.582136   \n3                        0.187031                        0.309682   \n4                        0.341663                        0.506308   \n\n   value__fourier_entropy__bins_5  value__fourier_entropy__bins_10  \\\n0                        0.079487                         0.419383   \n1                        0.891060                         1.336251   \n2                        0.948691                         1.397948   \n3                        0.600197                         1.022235   \n4                        0.866293                         1.327997   \n\n   value__fourier_entropy__bins_100  \\\n0                          2.000401   \n1                          3.019874   \n2                          2.576279   \n3                          2.654834   \n4                          2.760333   \n\n   value__permutation_entropy__dimension_3__tau_1  \\\n0                                        1.747535   \n1                                        1.706146   \n2                                        1.669552   \n3                                        1.638109   \n4                                        1.637482   \n\n   value__permutation_entropy__dimension_4__tau_1  \\\n0                                        3.015811   \n1                                        2.903657   \n2                                        2.772489   \n3                                        2.654572   \n4                                        2.680036   \n\n   value__permutation_entropy__dimension_5__tau_1  \\\n0                                        4.068979   \n1                                        3.936212   \n2                                        3.784472   \n3                                        3.644889   \n4                                        3.652981   \n\n   value__permutation_entropy__dimension_6__tau_1  \\\n0                                        4.555721   \n1                                        4.520418   \n2                                        4.409911   \n3                                        4.335833   \n4                                        4.350795   \n\n   value__permutation_entropy__dimension_7__tau_1  \n0                                        4.724480  \n1                                        4.747206  \n2                                        4.735843  \n3                                        4.686101  \n4                                        4.656301  \n\n[5 rows x 779 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>value__variance_larger_than_standard_deviation</th>\n      <th>value__has_duplicate_max</th>\n      <th>value__has_duplicate_min</th>\n      <th>value__has_duplicate</th>\n      <th>value__sum_values</th>\n      <th>value__abs_energy</th>\n      <th>value__mean_abs_change</th>\n      <th>value__mean_change</th>\n      <th>value__mean_second_derivative_central</th>\n      <th>value__median</th>\n      <th>...</th>\n      <th>value__fourier_entropy__bins_2</th>\n      <th>value__fourier_entropy__bins_3</th>\n      <th>value__fourier_entropy__bins_5</th>\n      <th>value__fourier_entropy__bins_10</th>\n      <th>value__fourier_entropy__bins_100</th>\n      <th>value__permutation_entropy__dimension_3__tau_1</th>\n      <th>value__permutation_entropy__dimension_4__tau_1</th>\n      <th>value__permutation_entropy__dimension_5__tau_1</th>\n      <th>value__permutation_entropy__dimension_6__tau_1</th>\n      <th>value__permutation_entropy__dimension_7__tau_1</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.290392</td>\n      <td>0.001766</td>\n      <td>0.001435</td>\n      <td>0.000011</td>\n      <td>-0.000032</td>\n      <td>0.002025</td>\n      <td>...</td>\n      <td>0.079487</td>\n      <td>0.079487</td>\n      <td>0.079487</td>\n      <td>0.419383</td>\n      <td>2.000401</td>\n      <td>1.747535</td>\n      <td>3.015811</td>\n      <td>4.068979</td>\n      <td>4.555721</td>\n      <td>4.724480</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.022239</td>\n      <td>0.000506</td>\n      <td>0.001323</td>\n      <td>-0.000021</td>\n      <td>-0.000008</td>\n      <td>0.000110</td>\n      <td>...</td>\n      <td>0.187031</td>\n      <td>0.490294</td>\n      <td>0.891060</td>\n      <td>1.336251</td>\n      <td>3.019874</td>\n      <td>1.706146</td>\n      <td>2.903657</td>\n      <td>3.936212</td>\n      <td>4.520418</td>\n      <td>4.747206</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.054796</td>\n      <td>0.001106</td>\n      <td>0.001827</td>\n      <td>-0.000011</td>\n      <td>0.000001</td>\n      <td>0.000627</td>\n      <td>...</td>\n      <td>0.307845</td>\n      <td>0.582136</td>\n      <td>0.948691</td>\n      <td>1.397948</td>\n      <td>2.576279</td>\n      <td>1.669552</td>\n      <td>2.772489</td>\n      <td>3.784472</td>\n      <td>4.409911</td>\n      <td>4.735843</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.042157</td>\n      <td>0.000932</td>\n      <td>0.001470</td>\n      <td>0.000014</td>\n      <td>0.000003</td>\n      <td>0.000269</td>\n      <td>...</td>\n      <td>0.187031</td>\n      <td>0.309682</td>\n      <td>0.600197</td>\n      <td>1.022235</td>\n      <td>2.654834</td>\n      <td>1.638109</td>\n      <td>2.654572</td>\n      <td>3.644889</td>\n      <td>4.335833</td>\n      <td>4.686101</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>0.0</td>\n      <td>-0.024980</td>\n      <td>0.000525</td>\n      <td>0.001215</td>\n      <td>-0.000027</td>\n      <td>-0.000007</td>\n      <td>-0.000144</td>\n      <td>...</td>\n      <td>0.341663</td>\n      <td>0.506308</td>\n      <td>0.866293</td>\n      <td>1.327997</td>\n      <td>2.760333</td>\n      <td>1.637482</td>\n      <td>2.680036</td>\n      <td>3.652981</td>\n      <td>4.350795</td>\n      <td>4.656301</td>\n    </tr>\n  </tbody>\n</table>\n<p>5 rows × 779 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Train and evaluate classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For later comparison, we train a decision tree on all features (without selection):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y[:500], test_size=.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "              precision    recall  f1-score   support\n\n           1       0.89      1.00      0.94        17\n           2       1.00      0.91      0.95        11\n           3       1.00      0.94      0.97        17\n           4       0.35      0.43      0.39        14\n           5       0.57      0.57      0.57        23\n           6       0.33      0.28      0.30        18\n\n    accuracy                           0.67       100\n   macro avg       0.69      0.69      0.69       100\nweighted avg       0.67      0.67      0.67       100\n\n"
    }
   ],
   "source": [
    "classifier_full = DecisionTreeClassifier()\n",
    "classifier_full.fit(X_train, y_train)\n",
    "print(classification_report(y_test, classifier_full.predict(X_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiclass feature selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now select a subset of relevant features using the `tsfresh` select features method.\n",
    "However it only works for binary classification or regression tasks. \n",
    "\n",
    "For a 6 label multi classification we therefore split the selection problem into 6 binary one-versus all classification problems. \n",
    "For each of them we can do a binary classification feature selection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Number of relevant features for class 5: 232/779\nNumber of relevant features for class 4: 214/779\nNumber of relevant features for class 6: 200/779\nNumber of relevant features for class 1: 233/779\nNumber of relevant features for class 3: 239/779\nNumber of relevant features for class 2: 170/779\n"
    }
   ],
   "source": [
    "relevant_features = set()\n",
    "\n",
    "for label in y.unique():\n",
    "    y_train_binary = y_train == label\n",
    "    X_train_filtered = select_features(X_train, y_train_binary)\n",
    "    print(\"Number of relevant features for class {}: {}/{}\".format(label, X_train_filtered.shape[1], X_train.shape[1]))\n",
    "    relevant_features = relevant_features.union(set(X_train_filtered.columns))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "289"
     },
     "metadata": {},
     "execution_count": 45
    }
   ],
   "source": [
    "len(relevant_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we keep only those features that we selected above, for both the train and test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_filtered = X_train[list(relevant_features)]\n",
    "X_test_filtered = X_test[list(relevant_features)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and train again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "              precision    recall  f1-score   support\n\n           1       0.89      1.00      0.94        17\n           2       1.00      0.91      0.95        11\n           3       1.00      0.94      0.97        17\n           4       0.32      0.50      0.39        14\n           5       0.58      0.48      0.52        23\n           6       0.43      0.33      0.38        18\n\n    accuracy                           0.67       100\n   macro avg       0.70      0.69      0.69       100\nweighted avg       0.69      0.67      0.67       100\n\n"
    }
   ],
   "source": [
    "classifier_selected = DecisionTreeClassifier()\n",
    "classifier_selected.fit(X_train_filtered, y_train)\n",
    "print(classification_report(y_test, classifier_selected.predict(X_test_filtered)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It worked! The precision improved by removing irrelevant features."
   ]
  },
  {
   "source": [
    "## Improved Multiclass feature selection\n",
    "We can instead specify the number of classes for which a feature should be a relevant predictor in order to pass through the filtering process. This is as simple as setting the `multiclass` parameter to `True` and setting `n_significant` to the required number of classes. We will try with a requirement of being relevant for 5 classes."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(400, 189)"
     },
     "metadata": {},
     "execution_count": 60
    }
   ],
   "source": [
    "X_train_filtered_multi = select_features(X_train, y_train, multiclass=True, n_significant=5)\n",
    "X_train_filtered_multi.shape"
   ]
  },
  {
   "source": [
    "We can see that the number of relevant features is lower than the previous implementation."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "              precision    recall  f1-score   support\n\n           1       0.94      1.00      0.97        17\n           2       1.00      1.00      1.00        11\n           3       1.00      0.94      0.97        17\n           4       0.35      0.43      0.39        14\n           5       0.68      0.65      0.67        23\n           6       0.56      0.50      0.53        18\n\n    accuracy                           0.74       100\n   macro avg       0.76      0.75      0.75       100\nweighted avg       0.75      0.74      0.74       100\n\n"
    }
   ],
   "source": [
    "classifier_selected_multi = DecisionTreeClassifier()\n",
    "classifier_selected_multi.fit(X_train_filtered_multi, y_train)\n",
    "X_test_filtered_multi = X_test[X_train_filtered_multi.columns]\n",
    "print(classification_report(y_test, classifier_selected_multi.predict(X_test_filtered_multi)))"
   ]
  },
  {
   "source": [
    "We now get slightly better classification performance, especially for classes where the previous classifier performed poorly. The parameter `n_significant` can be tuned for best results."
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
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